So that the two statements do not contradict each other, Statement 2 should read as shown below:
A chef mixes P ounces of 60% sugar solution with Q ounces of a 10% sugar solution to produce R ounces of a 25% sugar solution. What is the value of P?
[Statement #1] Q = 455 mL
[Statement #2] R = 650 mL
P = 60% sugar.
Q = 10% sugar.
R = the MIXTURE of P and Q = 25% sugar.
To determine the required ratio of P to Q, use ALLIGATION -- a very efficient way to handle MIXTURE PROBLEMS.
Step 1: Plot the 3 percentages on a number line, with the percentages for P and Q on the ends and the percentage for mixture R in the middle.
P 60%------------25%------------10% Q
Step 2: Calculate the distances between the percentages.
P 60%-----
35-----25%-----
15-----10% Q
Step 3: Determine the ratio in the mixture.
The required ratio of P to Q is equal to the RECIPROCAL of the distances in red.
P/Q = 15/35 = 3/7.
Since P/Q = 3/7, and 3+7=10, every 10 liters of mixture R is composed of 3 liters of P and 7 liters of Q.
Statement 1: Q=455
Since P/Q = 3/7, P = (3/7)Q.
Thus, P = (3/7)(455) = 195.
SUFFICIENT.
Statement 2: R=650
Since every 10 liters of mixture R includes 3 liters of P, P is equal to 3/10 of mixture R:
P = (3/10)(650) = 195.
SUFFICIENT.
The correct answer is
D.
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